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Last data update: 2014.03.03

R: Two-sample Hotelling's T-squared test

hotelling.test

R Documentation

Two-sample Hotelling's T-squared test

Description

Performs a two-sample Hotelling's T-squared test for the difference in two multivariate means

Usage

hotelling.test(x, ...)
## Default S3 method:
hotelling.test(x, y, shrinkage = FALSE, perm = FALSE,
                                 B = 10000, progBar = (perm && TRUE), ...)
## S3 method for class 'formula'
hotelling.test(x, data = NULL, pair = c(1, 2), ...)

Arguments

`x`	a matrix containing the data points from sample 1 or a formula specifying the elements to be used as a response and the grouping variable as a predictor
`y`	a matrix containing the data points from sample 2
`shrinkage`	if TRUE then Shaefer and Strimmer's James-Stein shrinkage estimator is used to calculate the sample covariance matrices
`perm`	if TRUE then permutation testing is used to estimate the non-parametric P-value for the hypothesis test
`B`	if perm is TRUE, then B is the number of permutations to perform
`progBar`	if TRUE and `perm` is TRUE then a progress bar will be displayed whilst the permutation procedure is carried out
`data`	a data frame needs to be specified if a formula is to be used to perform the test
`pair`	a vector of length two which can be used when the grouping factor has more than two levels to select different pairs of groups. For example for a 3-level factor, pairs could be set to c(1,3) to perform Hotelling's test between groups 1 an 3
`...`	any additional arguments. This is useful to pass the optional arguments for the default call from the formula version

Value

A list (which is also of class 'hotelling.test') with the following elements:

`stats`	a list containing all of the output from hotelling.stat
`pval`	the P-value from the test
`results`	if perm = TRUE, then all of the permuation test statisics are stored in results

Author(s)

James M. Curran

References

Hotelling, H. (1931). “The generalization of Student's ratio.” Annals of Mathematical Statistics 2 (3): 360–378.

Schaefer, J., and K. Strimmer (2005). “A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics.” Statist. Appl. Genet. Mol. Biol. 4: 32.

Opgen-Rhein, R., and K. Strimmer (2007). “Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach.” Statist. Appl. Genet. Mol. Biol. 6: 9.

Campbell, G.P. and J. M. Curran (2009). “The interpretation of elemental composition measurements from forensic glass evidence III.” Science and Justice, 49(1),2-7.

Examples

data(container.df)
fit = hotelling.test(.~gp, data = container.df)
fit

subs.df = container.df[1:10,]
subs.df$gp = rep(1:2, c(5,5))
fitPerm = hotelling.test(Al+Fe~gp, data  = subs.df, perm =  TRUE)
fitPerm
plot(fitPerm)

data(bottle.df)
fit12 = hotelling.test(.~Number, data = bottle.df)
fit12

fit23 = hotelling.test(.~Number, data = bottle.df, pair = c(2,3))
fit23

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Hotelling)
Loading required package: corpcor
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Hotelling/hotelling.test.Rd_%03d_medium.png", width=480, height=480)
> ### Name: hotelling.test
> ### Title: Two-sample Hotelling's T-squared test
> ### Aliases: hotelling.test hotelling.test.default hotelling.test.formula
> ###   hotel.test
> ### Keywords: htest
> 
> ### ** Examples
> 
> data(container.df)
> fit = hotelling.test(.~gp, data = container.df)
> fit
Test stat:  126.11 
Numerator df:  9 
Denominator df:  10 
P-value:  4.233e-09 
> 
> subs.df = container.df[1:10,]
> subs.df$gp = rep(1:2, c(5,5))
> fitPerm = hotelling.test(Al+Fe~gp, data  = subs.df, perm =  TRUE)
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Test stat:  4.6039 
Numerator df:  2 
Denominator df:  7 
Permutation P-value:  0.0221 
Number of permutations : 10000 
> plot(fitPerm)
> 
> data(bottle.df)
> fit12 = hotelling.test(.~Number, data = bottle.df)
> fit12
Test stat:  4.5041 
Numerator df:  5 
Denominator df:  34 
P-value:  0.002949 
> 
> fit23 = hotelling.test(.~Number, data = bottle.df, pair = c(2,3))
> fit23
Test stat:  57.519 
Numerator df:  5 
Denominator df:  34 
P-value:  1.332e-15 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>